**280 trigonometry questions.**

Consider two square matrices $A_1$ and $A_2$. Consider the following matrix involving matrix trigonometric functions:
\begin{equation}
M_1(t)=\begin{bmatrix} \cos(tA_1) & t\mathrm{sinc}(t A_1) \\ ...

I am using the following Solve code:
...

I am new to SE Mathematica, and search gives no answer; so here is my problem:
During the testing of my numerical library for quaternions with Mathematica (package Quaternions) I observed the ...

I am trying to evaluate (on Mathematica v.9) the integral
\begin{equation}
\int_0^x [\sin (x) \sin (2 y)-\sin (2 x) \sin (y)]^t \,\mathrm{d}y,
\end{equation}
where $t$ is an even, positive integer. ...

I have defined a function that produces a single negative impulse spanning -b to -a and a positive impulse spanning ...

When I enter the following Integral problem to Mathematica,
$$
\int \frac{1}{\sqrt{a²-x²}}\textrm{d}x
$$
The answer yielded by Mathematica is
$$
\arctan\left({\frac{x}{\sqrt{a²-x^2}}}\right)
$$
Rather ...

I have curve given by summing a small, finite series of Sinc functions, and I want to plot both the curve and its integral. In principle, it's easy:
...

As an intermediate step, consider the function:f[x_] := x Sin[Pi/x]I want to prove that this function is increasing for $x\ge 1$. This can be done with the ...

I have a table given byTable[
Evaluate[
Sum[(Sin[(2 π j x)/(r + 1)])/(r + 1), {j, 0, r}]],
{r, 1, 25}, {x, 0, 25}] /. Indeterminate -> 0The ...

I have the expressionSum[(2 j \[Pi] Sin[(2 j \[Pi] x)/(r + 1)])/(r + 1)^2, {j, 0, r}] == 0I want to find the roots in terms of ...

I’d like to use the TrigReduce function on a sum of n sinusoids to any power, and am running into an issue with Mathematica’s default ordering of symbols. Is there a way that I can specify an order ...

I have a problem with an indefinite integral which I solved using MMA in back in 2010 (must have been version 7 or 8) successfullly and it gave an elegant result. However, if I run it with MMA 11.3 (...

I have an impulse train given by(1 + Csc[(π x)/(1 + R)] Sin[(π (1 + 2 R) x)/(1 + R)])/(2 + 2 R)Because of the Csc, ...

I'm working with a trigonometric function, so I thought it would be convenient to set a condition to restrict the domain so I wouldn't have to specify it in the solve function each time. Here is a ...

Is there any way to force Mathematica to not use double and half angle formulae etc. when simplifying Trigonometric expressions?
For example,...

I am trying to convert a trigonometric expression likesinθ/(1 - cosθ)intocosecθ + cotθor
...

I would like to solve this equation:
$$-x\sin(x)=\cos(x)$$
But Solve in Mathematica doesn't work:
This system cannot be solved with the methods available to <...

Consider an impulse train1/(R + 1) + (Sum[Cos[(2 k π x)/(R + 1)], {k, R}])/(R + 1)For x=0 it's clear that this function ...

I have an impulse train of frequency R:1/(R + 1) + (Sum[Cos[(2 k π x)/(R + 1)], {k, R}])/(R + 1)For ...

The formula for a single impulse of amplitude $1$ at $x=r$ is given by
$$\frac {\sin (\pi (x-r))}{\pi (x-r)}$$
(In MathJax because it's a math formula.)
Formally, at $x=r$, this function evaluates ...

Consider the following inputAssuming[Element[y, Integers], (-1 + E^(I \[Pi] (x + y)))/(-1 + E^(I \[Pi] (x - y)))//FullSimplify] ...

I have this expression2 Csc[2 y[x2]] Sech[x[x2]]^2 (Cos[y[x2]]^4 Cosh[x[x2]]^8 Sin[y[x2]]^4)^(1/4)which is 1. But Mathematica doesn't do the simplification. I ...

My code returns this result involves trigonometric functions,
...

I want to plot the following function, where Rb is the variable (that has to be on the x-axis):
...

I have two trigonometric expressions. I would like to eliminate the fraction from my 2nd expression.
...

I have a simple trig equation:Clear[f, x]
f[x_] = Cos[2*x] - 3 Sin[x] + 2
Solve[f[x] == 0, x]I received a very long a complicated reply that I do not ...

I manipulate equations which are trigonometric equations in mechanics. In theses equations, the custom is to use only Cos, Sin and Tan functions and not the secant and cosecant functions.
To prevent ...

I am trying to figure out how to do the following exercise in Mathematica
Graph $y(t)= a \cos t + b \sin t - 0.5 \sin t$ on the interval $0 ≤ t ≤ 6\, π$

I am given a solution $v_1$(t)=$-e^{t/2}cost$ for a system of first order ODE and I am asked to verify this solution can solves the linear second order ODE in terms of $y_1$(t)
Here is the matrix ...

I want to define a function as suchg[n_] := Assuming[1<=x<=2, NSolve[n==-2 Cos[Pi x], x]]However the result comes out as a conditional expression, for ...

I want to generate (and eventually sample) a sine wave with a random frequency in the range [½, 1] (i.e. capture somewhere between half and one period of the waveform over the domain [0,1]).
The two ...

I am trying to integrate an equation that requires an angle term calculated using ArcTan[x,y]. A number of issues have been mentioned about ...

How can the following trigonometric system of equations be solved numerically?
...

I am new to this and I've plotted this:Plot[3 ArcSin[x + 4] - 16, but I don't know what/how to specify the range?

I want to solve the trigonometric equation :
$$(3-\cos 4x )\cdot (\sin x - \cos x ) = 2.$$
I triedSolve[(3 - Cos[4*x])*(Sin[x] - Cos[x]) == 2, x]It returns the ...

I'm trying to determine the angle x in the triangle shown below.
Given $\overline{DB}=\overline{DE}$
Given $\overline{AD}=\overline{DC}$
Given $\angle ADE=40^°$
Find $\angle DCB$
But I'm finding ...

I have a bunch of data to which I've assigned units using Quantity, including some angular measurements in degrees. I'd like to be able to use these measurements ...

To solve this problem just follow this rule or is there another possibility?Solve[(3 Sqrt[2])/Sin[60 Degree] == x/Sin[45 Degree], {x}]

I am trying to solve an equation in Wolfram Mathematica and I get different results although the equation is technically the same. I am really confused. so basically:
$\sin(2x) - \cos(2x)= 1$ is the ...

I am wondering why this simplification does not work,FullSimplify[Im[1/Sin[a]], Assumptions -> Element[a, Reals]]
(*Out[1]= Im(csc(a))*)while this does:<...

I have the following differential equation
...

This question must be too simple, but it confused me for several days. I want to know how can I do the following simplification using Mathematica:
For example, convert ...

Update
This bug has been fixed in v11.3.0.
And as @Carl Woll has pointed out, the imaginary part of Sin and negative sign of Cos...

I have a complex expression with real positive variables only.
Mathematica Input Style:
...

I have a coordinate system generated by :coord = Table[{x, y}, {x, 5}, {y, 5}]I would like to calculate ArcTan(y/x) and ...

There are at least a few non-overlapping triangles made by the lines in the following graphic, how would I isolate them?
...

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